#### Room 326

#### Local class field theory

#### Denis Benois

##### University of Bordeaux

*In this course we give a self-contained exposition of the local class field theory using the homological algebra. The local class field theory gives a description of abelian extension of local fields and their arithmetical properties. The following topic will be covered:*

1. Complexes and homology.

2. Derived functors

3. Cohomology and homology of groups.

4. Tate exact sequence

5. Local class field theory: main theorems

6. The theory of Lubin-Tate.

Done